CompletedGroupAlgebra.OpenFiniteQuotientTopology

5 sections | 9 files | 184 declarations

This module develops completed group algebras through finite quotient stages, transition maps, coefficient change, augmentation, comparison maps, and inverse-limit topology.

CanonicalMaps

1 files | 37 declarations | 27 Theorem | 10 Definition
The quotient map from the abstract group algebra \(R[G]\) to one \(C\)-indexed finite stage.

FiniteQuotients

1 files | 33 declarations | 25 Theorem | 7 Definition | 1 Abbreviation
An open coefficient ideal gives a continuous quotient map when the quotient is equipped with the discrete topology. This is the coefficient-side continuity used in Ribes--Zaless...

OpenFiniteComparison

1 files | 26 declarations | 19 Theorem | 7 Definition
The canonical map from the fixed-coefficient completed group algebra \(\widehat{R[G]}\) to the two-parameter limit \(\varprojlim_{I,U} (R/I)[G/U]\).

OpenFiniteLimit

5 files | 59 declarations | 32 Theorem | 4 Definition | 2 Abbreviation | 21 Instance
The zero element is defined coordinatewise as the compatible family of zero elements at all finite stages.

OpenFiniteQuotients

1 files | 29 declarations | 18 Theorem | 7 Definition | 3 Abbreviation | 1 Instance
The open coefficient ideals used in the kernel-neighborhood topology of Ribes--Zalesskii Section \(5.3\).